which graph contains the points of intersections satisfying this linear-quadratic system of equations? x^2+y^2=20 x-y+2=0
Accepted Solution
A:
Answer: There are two points of intersection (2, 4) and (-4, -2)Step-by-step explanation:x - y + 2 = 0 → x = y - 2Use Substitution Method:x² + y² = 20(y - 2)² + y² = 20 replaced x with (y - 2) y² - 4y + 4 + y² = 20 expanded (y - 2)²2y² - 4y + 4 = 20 added like terms2y² - 4y - 16 = 0 subtracted 20 from both sidesy² - 2y - 8 = 0 divided both sides by 2(y - 4)(y + 2) = 0 factoredy - 4 = 0 and y + 2 = 0 applied Zero Product Propertyy = 4 and y = -2Input the y-values into x = y - 2 to solve for x.y = 4; x = 4 - 2 y = -2; x = -2 - 2 x = 2 x = -4 (2, 4) (-4, -2)